Theorems · Theorem · ring theory

StarSubalgebra.map_iInf

∀ {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
  [inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : StarModule R A] [inst_6 : Semiring B] [inst_7 : Algebra R B]
  [inst_8 : StarRing B] [inst_9 : StarModule R B] {ι : Sort u_5} [Nonempty ι] (f : A →⋆ₐ[R] B),
  Function.Injective ⇑f →
    ∀ (s : ι → StarSubalgebra R A), StarSubalgebra.map f (iInf s) = ⨅ i, StarSubalgebra.map f (s i)

Defined in

Mathlib.Algebra.Star.Subalgebra

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringStarRingSemiringAlgebraStarRingStarModuleSemiringAlgebraStarRingStarModuleNonempty